The no hair theorem for black holes is found to apply even when they are surrounded by matter.
Fuzzy Wuzzy
According to general relativity, a black hole has three measurable properties: mass, rotation (angular momentum), and charge. That’s it. If you know those three things, you know all there is to know about the black hole. If the black hole is interacting with other objects, then the interactions can be much more complicated, but an isolated black hole is just mass, rotation and charge.